Geometry Lab
Surface Area of a Sphere
When a plane intersects a sphere so that it contains the center of the sphere, the
hemispheres
intersection is called a great circle. A great circle has the same center as the sphere,
and its radii are also radii of the sphere. Each great circle separates a sphere into two
congruent halves called hemispheres.
In this activity, you will use hemispheres and great circles to investigate the surface area
of a sphere.
Activity
Step 1 Cut a polystyrene ball along a great circle to create a
hemisphere. Place the hemisphere on a piece of paper
and trace around the edge to draw a circle. Then cut
out the paper circle.
Step 2 Fold the circle into eighths. Then unfold and cut the
eight pieces apart. Tape the pieces back together in the
arrangement shown at the right.
Step 3 Use tape to put the two pieces of the ball back together.
Then pin or tape the pattern to the sphere.
Analyze the Results
1. About how much of the total surface of the sphere was covered by
the pattern?
2. What is the area of the pattern in terms of r, the radius of the sphere?
Explain your reasoning.
3. Describe in words how you could find the total surface area of the sphere.
4. Write a formula that can be used to find the surface area of any sphere.
750 | Extend 12-7 | Geometry Lab: Surface Area of a Sphere
great circle
KeyConcept Surface Area of a Sphere
The surface area S of a sphere is
S = 4 πr 2, where r is the radius.
Words
S = 4πr
Symbols
Model
r
2
Exercises
Find the surface area of each sphere. Round to the nearest tenth.
5.
6.
11 cm
7.
9m
6 in.
8.
9.
3.2 in.
10.
15 mm
6.8 ft
13.
13 yd
8.4 ft
11.
12.
7.5 in.
14. SPORTS The table shows the approximate length of the
diameters of several regulation game balls.
Type of Ball
Diameter (cm)
baseball
3
a. Find the surface area of each ball. Round to the nearest tenth.
men’s basketball
24
b. About how many times greater is the surface area of a
regulation basketball than a regulation baseball?
soccer ball
22
softball
4
15. NATURE A hummingbird lays eggs that are nearly spherical.
If a hummingbird egg measures 1 centimeter in diameter,
what is the surface area of a hummingbird egg?
Find the surface area of each figure. Round to the nearest tenth.
16.
17.
7 mm
18.
8 in.
6.5 cm
10 in.
5 cm
5.5 mm
6.5 m
5 cm
connectED.mcgraw-hill.com
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